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We consider a general incompressible finite model protein of size M in its environment, which we represent by a semiflexible copolymer consisting of amino acid residues classified into only two species (H and P, see text) following Lau and Dill. We allow various interactions between chemically unbonded residues in a given sequence and the solvent (water), and exactly enumerate the number of conformations W(E) as a function of the energy E on an infinite lattice under two different conditions: (i) we allow conformations that are restricted to be compact (known as Hamilton walk conformations), and (ii) we allow unrestricted conformations that can also be non-compact. It is easily demonstrated using plausible arguments that our model does not possess any energy gap even though it is supposed to exhibit a sharp folding transition in the thermodynamic limit. The enumeration allows us to investigate exactly the effects of energetics on the native state(s), and the effect of small size on protein thermodynamics and, in particular, on the differences between the microcanonical and canonical ensembles. We find that the canonical entropy is much larger than the microcanonical entropy for finite systems. We investigate the property of self-averaging and conclude that small proteins do not self-average. We also present results that (i) provide some understanding of the energy landscape, and (ii) shed light on the free energy landscape at different temperatures.
A theoretical framework is developed to describe experiments on the structure of epitaxial thin films, particularly niobium on sapphire. We extend the hypothesis of dynamical scaling to apply to the structure of thin films from its conventional appli
An Ising--like model of proteins is used to investigate the mechanical unfolding of the Green Fluorescent Protein along different directions. When the protein is pulled from its ends, we recover the major and minor unfolding pathways observed in expe
Aggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differ
Many theoretical expressions of dissipation along non-equilibrium processes have been proposed. However, they have not been fully verified by experiments. Especially for systems strongly interacting with environments the connection between theoretica
An exact analytical diagonalization is used to solve the two dimensional Extended Hubbard Model for system with finite size. We have considered an Extended Hubbard Model (EHM) including on-site and off-site interactions with interaction energy U and